| 商空间的近端点和近严格凸性 |
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| 引用本文： | 段丽芬,崔云安.商空间的近端点和近严格凸性[J].兰州理工大学学报,2004,30(5):133-135. |
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| 作者姓名： | 段丽芬 崔云安 |
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| 作者单位： | 通化师范学院,数学系,吉林,通化,134002;哈尔滨理工大学,应用科学学院,黑龙江,哈尔滨,150080 |
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| 基金项目： | 国家自然科学基金(10171025) |
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| 摘 要： | 证明了商空间X/M单位球面上的点x]为近端点的充分条件是x]与X的单位球面的交集中存在近端点,其中,M是Banach空间X的可逼近子空间.进而推出了Banach空间X以它的可逼近子空间M为模的商空间X/M对X的近严格凸性的继承性.同时,以一般Orlicz空间为例,说明了上述结论成立可逼近条件是必要的.
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| 关 键 词： | 商空间 近端点 近严格凸 可逼近 |
| 文章编号： | 1000-5889(2004)05-0133-03 |
| 修稿时间： | 2003年12月1日 |
On nearly extreme point and nearly strict convexity of quotient space |
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| DUAN Li-fen,CUI Yun-an.On nearly extreme point and nearly strict convexity of quotient space[J].Journal of Lanzhou University of Technology,2004,30(5):133-135. |
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| Authors: | DUAN Li-fen CUI Yun-an |
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| Institution: | DUAN Li-fen~1,CUI Yun-an~2 |
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| Abstract: | It is proved that the sufficient condition of a point x] on a unit spherical surface in quotient space X/M being a nearly extreme point is the existence of a nearly extreme point in the intersection of x] and unit spherical surface of X.Here M is an approximatible subspace of Banach space X.Then,the succession to nearly strict convexity by the quotient space X/M,for which the subspace M is taken as a module in Banach space X,is derived.Meanwhile,the generalized Orlicz space is taken as an illustration to show that,for the validity of forgoing conclusion,the condition of approximatibility is necessary. |
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| Keywords: | quotient space nearly extreme point nearly strict convexity approximatibility |
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